Differentiation: Quotient rule [L8]

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Abbi Mullins 6 years, 8 months ago

Created this as a copy of Harry's copy of Differentiation: Quotient rule.

Name	Status	Author	Last Modified
Differentiation: Quotient rule	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Harry's copy of Differentiation: Quotient rule	draft	Harry Flynn	09/05/2018 14:12
Differentiation: Quotient rule [L8]	draft	Abbi Mullins	24/07/2018 14:12
Luis's copy of Differentiation: Quotient rule	draft	Luis Hernandez	30/11/2018 18:59
Derivada aplicando la regla del cociente	Ready to use	Luis Hernandez	30/03/2020 14:41

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Question statement

Differentiate the following function $f(x)$ using the quotient rule.

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			Name	Type	Generated Value

a	integer	5
c	integer	8
b	integer	8
d	integer	-5
s2	integer	-1
s1	integer	1
det	integer	-89
c1	integer	8

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$\simplify[std]{f(x) = ({a} * x+{b})/({c}*x+{d})}$

$\displaystyle \frac{df}{dx}=\;$ Unnamed gap

Advice

The quotient rule says that if $u$ and $v$ are functions of $x$ then

$\simplify[std]{Diff(u/v,x,1) = (v * Diff(u,x,1) - u * Diff(v,x,1))/v^2}$

For this example:

$\simplify[std]{u = ({a}x+{b})}\Rightarrow \simplify[std]{Diff(u,x,1) = {a}}$

$\simplify[std]{v = ({c} * x+{d})} \Rightarrow \simplify[std]{Diff(v,x,1) = {c}}$

Hence on substituting into the quotient rule above we get:

$\begin{eqnarray*} \frac{df}{dx}&=&\simplify[std]{({a}({c}x+{d})-{c}({a}x+{b}))/({c}x+{d})^2}\\ &=&\simplify[std]{({a*c}x+{a*d}-{c*a}x-{c*b})/({c}x+{d})^2}\\ &=&\simplify[std]{{det}/({c}x+{d})^2} \end{eqnarray*}$

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This question is used in the following exams:

Test 1 Milena by Milena Venkova in Milena's workspace.
MATH1602 Quiz 3 by Blathnaid Sheridan in Blathnaid's workspace.
MATH1902 Quiz 1 Differentiation by Blathnaid Sheridan in Blathnaid's workspace.

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Abbi Mullins 6 years, 8 months ago

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Differentiation: Quotient rule [L8]

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Abbi Mullins 6 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`